everyone has their preferences in terms of which type of carrier (and fabric) they prefer.
for a newborn i'd do a ring sling with a linen or linen blend (i make these for every baby shower gift!). depending on your size you'll need 2-2.5 yards. there are a lot of different shoulder styles, as someone mentioned there are lots of good directions on the sleeping baby website.
for a newborn wrap the best is either a stretchy jersey t-shirt type of material, or else cotton gauze/crinkle cotton. depending on your size you'll need somewhere in the neighborhood of 5-6 yards. best to buy more, you can always hem it down. then you can cut it length-wise down the middle and have two carriers for the price of one.
mei tai's and podaegis aren't hard to make either, and will probably be more comfortable for the long-haul with heavier/older babies.
i will say, however, that sometimes it's a good idea to also look around and see what gently used carriers are going for. you can often get a used babyhawk or kozy for $40-$45ppd and i see ring slings for $15-$25 and pouches for like $10-$15 all the time. i saw an ellaroo woven wrap here on the TP the other day for $25. i'm prone to buy really nice fabric when i go to a fabric store, so sometimes i think my DIY's cost more than gently used commercial carriers LOL